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Disclaimer: I am not a student of psychology, just an interested guy - but here goes anyway...

IQ tests usually contain dozens of questions and take considerable time. I think this is because such tests have to differentiate between a great diversity of intelligence levels.

Now, I wonder if a test could be devised such that you answer a fraction of a number of questions associated with the usual IQ test, and the test result is yes, your IQ is between 100 and 120, or no, your IQ is outside of this range.

This could be useful, if someone is intelligent, but has problems with attention, or in some kind of survey setting, where people don't have a lot of time.

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  • $\begingroup$ That's really interesting! So you are saying that such a short test would have a noticeably lower precision than a traditional IQ test? E.g. it would be analogous to saying "yeah, the weather is a little chilly" as opposed to saying "the temperature is 42.3 degrees F with a wind chill factor of..." $\endgroup$ – Robert Columbia Mar 11 '17 at 23:27
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Yes, what you say is entirely possible. If precision is not as much of an issue, it is possible to devise a test (of anything, not just a test of IQ) which would return a score of, say, 115 plus or minus 10 points. It could also return a yes/no answer to a question such as "is the score inside the range 100..120.

One person who explore such question is Laurencelle, 2015, Le différentiel de sélection multiple [in french] The Quantitative Methods for Psychology, 11(3), 174-188. doi http://dx.doi.org/10.20982/tqmp.11.3.p174

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All else being equal, more items on an intelligence test means better reliability. As reliability increases, the standard error of measurement decreases.

Good intelligence tests might have a standard error of 3 where the mean is 100 and the standard deviation is 15 (i.e., a fifth of a standard deviation). And we often talk about 95% confidence intervals which is about plus or minus two standard errors. So by your example if we say we want to know that a 95% confidence interval of a score of 110 is 100 and 120. This implies a standard error of 5 (i.e., plus of minus 2 * 5).

You may want to check out the Spearman-Brown prediction formula. It makes predictions about expected reliability of a test based on number of items assuming you know the reliability for a given number of items.

This article looks like a reasonable introduction to standard error of measurement and includes relevant formulas: https://jalt.org/test/PDF/Brown4.pdf

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